1,261 research outputs found
Exact solution for many-body Hamiltonian of interacting particles with linear spectrum
The exact solution of the Schr\"odinger equation for the one-dimensional
system of interacting particles with the linear dispersion law in an arbitrary
external field is found. The solution is reduced to two groups of particles
moving with constant velocities in the opposite directions with a fixed
distance between the particles in each group. The problem is applied to the
edge states of the 2D topological insulator.Comment: 4 page
Influence of gravitational field on quantum-nondemolition measurement of atomic momentum in the dispersive Jaynes-Cummings model
We present a theoretical scheme based on su(2) algebra to investigate the
influence of homogeneous gravitational field on the quantum nondemolition
measurement of atomic momentum in dispersive Jaynes-Cummings model. In the
dispersive Jaynes-Cummings model, when detuning is large and the atomic motion
is in a propagating light wave, we consider a two-level atom with quantized
cavity-field in the presence of a homogeneous gravitational field. We derive an
effective Hamiltonian describing the dispersive atom-field interaction in the
presence of gravitational field. We can see gravitational influence both on the
momentum filter and momentum distribution. Moreover, gravitational field
decreases both tooth spacing of momentum and the width of teeth of momentum.Comment: 21 pages, 8 figure
Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer
We present an optomechanical displacement transducer, that relies on three
cavity modes parametrically coupled to a mechanical oscillator and whose
frequency spacing matches the mechanical resonance frequency. The additional
resonances allow to reach the standard quantum limit at substantially lower
input power (compared to the case of only one resonance), as both, sensitivity
and quantum backaction are enhanced. Furthermore, it is shown that in the case
of multiple cavity modes, coupling between the modes is induced via reservoir
interaction, e.g., enabling quantum backaction noise cancellation. Experimental
implementation of the schemes is discussed in both the optical and microwave
domain.Comment: 5 pages, 3 figures. Revised and amended versio
QND and higher order effects for a nonlinear meter in an interferometric gravitational wave antenna
A new optical topology and signal readout strategy for a laser interferometer
gravitational wave detector were proposed recently by Braginsky and Khalili .
Their method is based on using a nonlinear medium inside a microwave oscillator
to detect the gravitational-wave-induced spatial shift of the interferometer's
standing optical wave. This paper proposes a quantum nondemolition (QND) scheme
that could be realistically used for such a readout device and discusses a
"fundamental" sensitivity limit imposed by a higher order optical effect.Comment: LaTex, 17 pages, 3 figure
Phase diffusion pattern in quantum nondemolition systems
We quantitatively analyze the dynamics of the quantum phase distribution
associated with the reduced density matrix of a system, as the system evolves
under the influence of its environment with an energy-preserving quantum
nondemolition (QND) type of coupling. We take the system to be either an
oscillator (harmonic or anharmonic) or a two-level atom (or equivalently, a
spin-1/2 system), and model the environment as a bath of harmonic oscillators,
initially in a general squeezed thermal state. The impact of the different
environmental parameters is explicitly brought out as the system starts out in
various initial states. The results are applicable to a variety of physical
systems now studied experimentally with QND measurements.Comment: 18 pages, REVTeX, 8 figure
Measuring nanomechanical motion with an imprecision far below the standard quantum limit
We demonstrate a transducer of nanomechanical motion based on cavity enhanced
optical near-fields capable of achieving a shot-noise limited imprecision more
than 10 dB below the standard quantum limit (SQL). Residual background due to
fundamental thermodynamical frequency fluctuations allows a total imprecision 3
dB below the SQL at room temperature (corresponding to 600 am/Hz^(1/2) in
absolute units) and is known to reduce to negligible values for moderate
cryogenic temperatures. The transducer operates deeply in the quantum
backaction dominated regime, prerequisite for exploring quantum backaction,
measurement-induced squeezing and accessing sub-SQL sensitivity using
backaction evading techniques
Optical noise correlations and beating the standard quantum limit in advanced gravitational-wave detectors
The uncertainty principle, applied naively to the test masses of a
laser-interferometer gravitational-wave detector, produces a Standard Quantum
Limit (SQL) on the interferometer's sensitivity. It has long been thought that
beating this SQL would require a radical redesign of interferometers. However,
we show that LIGO-II interferometers, currently planned for 2006, can beat the
SQL by as much as a factor two over a bandwidth \Delta f \sim f, if their
thermal noise can be pushed low enough. This is due to dynamical correlations
between photon shot noise and radiation-pressure noise, produced by the LIGO-II
signal-recycling mirror.Comment: 12 pages, 2 figures; minor changes, some references adde
Conversion of conventional gravitational-wave interferometers into QND interferometers by modifying their input and/or output optics
The LIGO-II gravitational-wave interferometers (ca. 2006--2008) are designed
to have sensitivities at about the standard quantum limit (SQL) near 100 Hz.
This paper describes and analyzes possible designs for subsequent, LIGO-III
interferometers that can beat the SQL. These designs are identical to a
conventional broad-band interferometer (without signal recycling), except for
new input and/or output optics. Three designs are analyzed: (i) a
"squeezed-input interferometer" (conceived by Unruh based on earlier work of
Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is
injected into the interferometer's dark port; (ii) a "variational-output"
interferometer (conceived in a different form by Vyatchanin, Matsko and
Zubova), in which homodyne detection with FD homodyne phase is performed on the
output light; and (iii) a "squeezed-variational interferometer" with squeezed
input and FD-homodyne output. It is shown that the FD squeezed-input light can
be produced by sending ordinary squeezed light through two successive
Fabry-Perot filter cavities before injection into the interferometer, and
FD-homodyne detection can be achieved by sending the output light through two
filter cavities before ordinary homodyne detection. With anticipated technology
and with laser powers comparable to that planned for LIGO-II, these
interferometers can beat the amplitude SQL by factors in the range from 3 to 5,
corresponding to event rate increases between ~30 and ~100 over the rate for a
SQL-limited interferometer.Comment: Submitted to Physical Review D; RevTeX manuscript with 16 figures;
prints to 33 pages in Physical Review double column format. Minor revisions
have been made in response to referee repor
Speed Meter As a Quantum Nondemolition Measuring Device for Force
Quantum noise is an important issue for advanced LIGO. Although it is in
principle possible to beat the Standard Quantum Limit (SQL), no practical
recipe has been found yet. This paper dicusses quantum noise in the context of
speedmeter-a devise monitoring the speed of the testmass. The scheme proposed
to overcome SQL in this case might be more practical than the methods based on
monitoring position of the testmass.Comment: 7 pages of RevTex, 1 postscript figur
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